Arc scriber



April 25, 1950 w. E. THlBoDEAU ARC scRIBE 2 Sheets-Sheet 2 Filed July 13, 1945 y. A l

Wi Hna E- T11-ih n d Emu @3M W1K MMJJM@ www Patented pr. 25, 1495i() ARC SCRIBER Wilfred E. Thibodeau, Franklin Township,4 Summit County, Ohio Application July 13, 1945, Serial No. 604,952

\ (Granted under the act of March 3, 1883, a's

' amended April 30, 1928; 370 0. G. 757) Claims.

The invention described herein may be manufactured and used'by or for the Government for governmental purposes without the payment to me of any royalty thereon. l

This invention relates to devices for generating a circular arc from a point on the radius of itscircle other than the true center.

' The vinvention represents an improvement over my copending application Serial No. 597,925 filed June 6, 1945, now Pat. No. 2,499,427, granted March '7, 1950. Therein it was shown that the polar coordinates of an arc were related to the minimum polar distance as follows and it was further shown that the denominator of the right hand member of the equation is solvable by a set of articulatedvarms having effective lengths of n and nA respectively where n is any number and R being the radius ofthe arc and ro the minimum polar distance from the polar origin.

The present invention materializes the polar coordinate by viewing Equation 1 as a constant product of two variables such that TD=ruDn=lc- Thus, if two intercepts on a straight line are varied inversely so'that their product remains constant while at the same time one intercept is varied as a function of the angleof rotation of said line about a xed point thereon in accordance with the aforesaid denominator of the right hand sideof Equation 1, then a terminus of the other intercept will generate the arc of a, circle having a radius determined by the particular value of A to the scale selected.

It istherefore an object of the invention to 'provide an instrument operable to generate a true arc of a circle having its center at a remote, inaccessible or inconveniently located point, by setting the sc riber at any given distance from any chord.

Another object is to provide an instrument for generating or describing the arclo'f a circle of long radii from a point on a. radius of such circle other 'than its true center.

.A further object .is to provide an instrument of thetype mentioned that is in the general .form of and usable inthe general manner of. an ordinary pair of drawing Compasses. Y v y A still further object is toprovidean Varc-gen,- erati-ng. instrument that is accurate,relativelyinT 2 expensive, and easy to construct and operate while at the same time adjustable for a wide range of radii. A

Other objects and advantages will become apparent as the description proceeds.

i In the drawings:

Fig. 1 is a plan view of one form of the improved instrument with the parts shown in the relation they will assume at the start of a curveplotting operation. Y A

Fig. 2 is an elevational view looking from right to left, Fig. 1, with the parts in initial adjustment, Y

Fig. 3 is a section taken upon the line 3-3, Fig. 1, and showing more particularly the means for fixing the instrument in adjusted position,

Fig. 4 is a view corresponding to Fig. 1 .but showing the parts in the relationlthey assume during the generation of an arc,

Fig. 5 is a view showing an adjustable pivot whereby the eiective length of onev of the sides of the basic triangle may be varied,

Fig. 6 is an end view looking in the direction of the arrow, Fig. 5, with the adjusting lever removed for greater clarity of illustration,

Fig. 7 is a plan view of another species wherein `'initial adjustment is elected by a special pivot joint interconnecting the arms of the instrument, Fig. 8 is an enlarged section taken on the line 8-8 of Fig. 7 and showing the construction of the pivot point,

Fig. 9 is a perspective view of another species of the invention in which the instrument is con, structed in the general form of a pair of drawing compasses,

Fig. 10 is a sectional View of a modified form o1' universal mounting for the legs of the instrument shown at Fig. 9, and Y Fig. 10a is a fragmentary sectional view, showing a modication'of the arrangement of Fig. 1Y0. In Figs. 1 to 4, inc., I have shown a form of the improved instrument wherein 1 identies a link of unit effective length to any convenient scale, adapted to be xed Vin position upon a surface upon which an arc is to be described. Fixation at one end is effected by a headed pivot screw 2 having a pointed or sharpened end. The other end is slotted to receive a relatively thin portion of a link 3 of eiiective length A. The links I and 3 are pivotally connected by a pivot bolt 4 having Ya xation point'i extending from its head and held in place by a nut 6. Aguide member] consists of a straight link 8 having its ends slotted, as at 9 and I0 and being pivoted on the smooth shank'portion Vof `pivot 2 at the junction of said portion is slightly greater in lengtlgiA than, the..

thickness of guide member I3 so that whenfwing nut I1 is turned down, arm II is rmly clamped to bolt I6 to x the point of pivoting of-member I3. At the same time, said member may. freely.. pivot on the bolt.

The end of link 3 oppositeeits .connection'tolunit7 link I, has the same thicknessas linkt and isapertured to receive a. pivot bolt I8 that also passesfthrousn slot@ lltn1s8feand-slet. Isin arm 15, tetherebrf mat.. iai. rsection. oi link 8 and arm I5 at a distance from pivot bolt t equal.. bathe. rredetennineddistance A. Furthermore it will be notedithatlbecauseof the. .XatiOn point when the instrument is in operatingposition, .the .belt` lavis-constrained to a Circulanpathahout theaxis. of holt 41.

The. linka.. It and arm: .I @intersect and the inter.- section may be materialized byascriber or stylus elemental! includinaa:barrel-12;I....Eia 2, having a smeethly-iittinsthe slctsin una s .and arm I4 and held in position by a cap 22 threaded-.onto ncnd. or.. barrel 2.1;, The-'barrel' has a central axial.. here f or; receiringaagleadf onstylus. 23, and an adiustngzscrew. 24 threadedintoeapz and may beturned down tofeedtheflead 23- forwardly, asxdesired... Indicatingv graduations 2.5 maybe provided along one .;.edge of:,lnk^8 f .or.the purpose of settingithe .radiusdesired; The.; Spees; insti describedoperatesupon the principle that the. altitudef: atriangle'withY right angled'. apex is the; mean proportional.v between the segment-scf the base;.ceterr'nined by thealtif tude. Hence.` 4Eq1.ia'.tion 2' written. in the. form zfnsroDoif-k issatsed for allipositi'onsof: the instrument since for each-.positiom tlfieproduct. oi' the. distances D betweenf theaxis of: pivotv 2. and bolt I8, and 1'.- betweenzpivotlland stylus element isrconstant. Hence itrisnecessary only to materialize the distance D in accordancewithde: nominator. on'the right' handside'offEquation 1 tofobtain: the distance r, of Equation-1. It was fully explained inlmy. prior ccp-pending application identied above that where thev effective length oi'flink- I is made equalitounit distance to the 4.scale selected, and thej effec-tive length of link 3 is made egual to Ag to the same scale, `and link Iremainsfixed" duri-ng an, arc-describing operation while link 3` rotatesY about its pivot axis with link I the distance between the remote ends. off'the two links is given- `by thei aforesaid denominator of'Equation 1-7. p Y

The operation-ofthe: instrument will be clear from the foregoing-'- description;4 Usually it will bevdesiredf to describe an` aro of known radius ish-rough a point lying uponfa certain radius,- the true center of theearc beinginaccessible or inan inconveniently" located positionsuch as Y outside of the confinesof a. drafting board.V The instrument isadjustedso'that links I, 3 and 'are in alignment; as shown inl Fig, 1j, wing nutV I'I is loosened' and 'guide member I3isfg-iven av combined translation along slotf IZ'f-and'rotation about bolt I8 the know-'n on desired radius'is indi# cated upon scale 25 by an edge of arm I 4. The wing nut is then tightened to x bolt I6 in adjusted position along slot I2. Next the instrument is positioned with scriber or stylus 23 on the point through which the arc is to pass and with the aligned axes of and. .8, extending along; theradiusof the; arcfthrugh such point. The xation points of link I are forced into the Supporting surface and guide member 1 is rotated about screw 2. Fig. 4 shows the position of the parts-1A after the are L has been partly described. ltwillbenoted that, during the describing procedure pivot bolt' I8 slides along slots I0 and I9 to decrease the distance between pivots 2 and I8 nzaccordanceawithithe basic formula of Equation 1 whileconcomitantly therewith the distance between pivot 2 and stylus 23, that is, the value 1',

vis;i..ncleaseli in. the. proper ratio such that the stylusforv scriberZtv describes the desired are. It will be understood that the instrument operates equally. Wellin .either .tbearst Qr. second. quadrants.r -and be; swung sountercleckwiseor clvckwise. asdesired.; t0 describe@ complete: are

Figs. 5 and 6 show a cons notion.wherebyv the eietiveleneth @fflinlvm be varied. In these 3f identities-- aiirik Garrespvndiria t0. link 3 0f FgS- Maasdam n@ Z1 in. its end.. This Slet maw@ 0f Q ti0aa1-shaeesuitable i@ guide ai rivet blo.. ,2M "tranSlatiQn-theref along- A Divot ISS' simil n urpaseandfuncf tion to pivot bolt i8, Eig secured withinY an aperture. in block 28., with its shank.: projecting.

by screws 29 acrossthe open end of slot 21 and swiveled at oneendtozf-bloclc 28 and having its @9171er GnfSQuWiw-Q; dehablyil-ceve an ad* justine awash. .5115. asalei. mar-'te provided along slot.2 11or coactioxr withgan indicator mark uponvblocli 28;. t0 enable accurate determination of the effective length of link 3. When such a. construction is employed slot I0, is of course, made suiiiciently lon'fg. ,toA accommodate the maximum outward adjustment of block 28. The va-.lueef tba effective.f1rne-th` er lin-.la .Sfissiven by l. lila wlierelt is: the radius ofV the circle. and m is the minima height of, the are, Y

Fiss., T arid-811. have. shvvl another; species of the invention wherein. iidentiies alink hav.. line Slots. 3| and. 3.2. adjacent-opposte ends.. and a,.pivo,t,screw,33linterme elfits ends; Screw 3 3 has a. 1T1 ati lr11 point Sini .ar tofthatof screw 2. Eigl. .Avirstarmvis pivQtedat-One end upon. Screw 3.3; and, has aslot farmedin. its other. end.. #Second .liisp Qtedatoljle and 1111011. a pivot bolt 3T slidabiynttma signa?. 4At its other end arm. 3.6. has. a Slot Athi-rd.- arm. 391' iS riveted. at. one'. end.' ur ,2f-.- Scriberor stylus e1e= ment- 4,0.. that `.naar b.. identical.. with. element. 20 usedin .th-.species ofK Arm. Szlkewise has a; Sinti! and a. special pivot. element passes through the superposedislots 35, 38 andiil. to pivQtallX andslidably assiate. the A The rivm.. element is Shawn. iii-Fia. 8.' and. in,- cliides, a; drstsleeve illgbavins .a ansat its lower end of a size to t between thesjhoulderel edges .0f .slot 35. and. als). having its'. @rosita and threads@ ...The steelt/e.. of Susient ,length to acomrncdate washeriiarid'nut; 4;@ so. that., when the'vluv is turns@ dmvrithe sleeveisrmlr clamped l0 am .314" 'ltstedlpe 1.01.1 along slet-35i A.' scqfdsleeve ilts Withinsl'eeve 42 `between the upper shouldered walls of arm 39.

This sleeve 45 has a length such that its plain upper end extends a few thousandths of an inch abovethe', adjacent end of sleeve 42. A third sleeve 46l`flts within sleeve 45 and has a flanged lower.` end slidably fitting between the lower shouldered walls of slot 4i and a threaded upper end projecting about the adjacent end of sleeve 45. A nut 41 is threaded upon sleeve 46 so that, when turned down, the flanges upon sleeves 45 and 46 are drawn together to clamp arm 39 therebetween and fix the axis of the pivot in adjusted -position along slot 4I. A Vfourth sleeve 48 fits within sleeve 46 and has a flange at its lower end 'fitting between the shouldered walls ofslot 38 in arm 36. A pivot bolt 49 fits within sleeve 48 and has a head 59 engagingthelower surface of arm 36 and a threaded upper end receiving a washer 5I and nut 52. Sleeve 48 projects a few thousandths of an inch above the adjacent end of sleeve 46 so that when nut 52 is turned down,

effected, as desired, to clamp all links against ,sliding rrelatively to the pivot axis, or to permit one or two of the links to slide while the others are clamped to prevent such sliding.

A unit vlink 53 is `pivoted at one end upon pivot vscrew 33'and at its other end is pivotally connected with rotating link 54 by means of a pivot .bolt 55. .The latter bolt may be identical with 4 bolt 4, Fig. 4, so that when its fixation point, as well as that of screw 33 is forced into the supporting surface, link' 53 is held in iixed position upon the surface. The other end of link 54 is pivotally associated with bolt 31. It will be understood that links 53 and 54 have effective lengths, that is lengths between pivot axes, determined as fully explained in my copending application previously identied.' If desired a scale of radii of arcs to be drawn may be applied to link 39 along slot 3|, for coaction with an indicator on stylus element 49, to gauge the initial or starting position of the stylus relatively to said link.

In use, the pivot 59 is set in slot 35 to give convenient lengths to arms 36 and 39 to reach the yextremitiesA of the desired arc. The eiiective lengths of arms 36 and 39 should be equal. Pivots 33 and 55 are now xed in the line of the minimum height of the desired arc with 33 at the foot of said height, and pivot 40 is set at the desired value of ro. Link 39 is then rotated about 33 as a center. As such rotation takes lplace, the bolt 31 slides along slot 32 because of the continuous deformation of the triangle determined by Vlinks 53 and 54. Since this triangle and that determined by arms 34 and 36 have a side in common, and since the eifective lengths of the arms 34 and 36 are now fixed, the deformation of theA triangle determined thereby results in a change in the'altitude thereof, that is, the perpendicularV distance of theV axis of bolt 49 from link 39. Inasmuch as arm 39 has its effective length fixed at this time. the aforesaid change is accommodated by a sliding movement of element 49 along slot 3|. The parts are shown yalsoxoui pivot pin 6i.

`pin 6l between the arms of yoke 69.

6 in dotted lines in the relation they assumeduring the generation of an arc L.

This form is based on the geometric principle that intersecting chords of a circle present segments having a constant product. Obviously the parameter determining this constant product is Vsolely the distance of the point of intersection from the center of the circle. Thus, in Fig. '1, since-arms 36 and 39 remain constant and equal, the arm 39 between pivots 31 and 49 is always a chord of a circle having a radius equal to the eiective lengths of arms 36 and 39. And since the length of arm 34 is fixed the point of intersection of the various' chords (i. e. pivot 33) is equidistant from the center of the circle and the instrument reiiects the geometric premise set forth above.

Fig. 9 shows a form of the invention generally resembling a pair of Compasses wherein the arms of a yoke have aligned apertures mounting a Three legs 62, 63 and 64 have enlarged apertured ends pivotally mounted upon The leg 63 is formed in two sections 65 and 66. As

' shown, section 65 has an axial bore within which the other section 66 is slidable.

A set screw 61 is provided in section 65 to secure the sections in axially adjusted positions. The lower end of section 66 is formed with a ball 19 received within a spherical socket formed in the end of l,reduced and apertured to smoothly it within slot 12 and to pivot on pin 1|. The other end 'of link 12 is enlarged to provide a socket for a ball 13 upon the lower end of leg 62 whereby this leg may pivot universally with respect to link 12. The leg 64 is formed as a conventional scriber leg' of a compass and may have a sleeve 14 adapted when turned down, to grip a scri'ber 15 in axially adjustedposition. The effective lengths of 62 and 64 areequal. The section 66 may be screwthreaded as shown at 16 for fine adjustment into upper member 65. In use, the set screw is loosened, scriber 15 is set at the proper value of ro and the set screw then tightened. The scriber may be moved by screwing section 6'6 into 65. Set screw 61 is then tightened. Now with links 68 and 12 in alignment on the radius of the minimum height of the arc and with all parts substantially in the relation shown at Fig. 9, the instrument is swung about leg 65. During this movement link 12 moves about pivot pin 1I so that the distance between the centers of balls 19 and 13 satises the terms of the basic equation. Furthermore, the aforesaid distance varies reciprocally with the distance between ball 19 and scriber 15 so that asscriber 15 rotates, its distance from the center of ball 19 is continuously changed to traverse the arc of a circle of the desired radius.

In Fig. 10 I have shown a construction for universally mounting the legs 62 and 63, Fig. 9, where maximum accuracy is necessary or desired. In this ligure 62 indicates a leg that may correspond to leg 62, Fig. 9. This leg has a plate attached to its lower end and formed as a portion of a spherical shell with center at C. A circular base plate 19 has a. central core 82 having its outer surface formed as a portion of a. sphere with center,`

vanimations-1 t aaO-: Aesh'elliiaz;forment-as.avportionzoltheasur:- face of a sphere Witlrzeenteir atuC-isssecuredto '.plate.- 'I 9. This-shell hastavoircular: openingy 84 therein slightly-'less insangular extenirftl'ianir plate 1.8i andiszwaced irornecore;d2.:bysrradialadistance tio-afford' a. smooth sliding'iiit: of-.tplatel A'l8r therebetween., Bythesconstruction shown,..leg 62'! is universally' mounted abouti'a.y center-lying; in the supporting surface sov vthai', ian'yf v errorl otherwise introduced byhaving said centersomewhatabove the surface; isobviatedl.; It Willibe` understood that a. similar mounting::issfcontemplated for leg 63,: Eg..9;

Thus: in: Fig. .laathere is;.shownfa.portion; of a link 12".' correspondingto link. T2 in Fig: 9. Correspending; to what isl shoum in-ctheecaseof Fig.. 5, the link 12 is slotted as at IIU to receivefas'slidr- 'block 83'.; This block?. performs: the same function as; sh'ell s-inrliig'.: :10'in thatxit accommodates the spherical. shell segment' 18. Theelatter slides onra partial spheref'fi W.l"1ich;,.;inv this case, isattachedito block B`3..'fas atlziZ.. A screw Hill has a head .H6 insertablea'na.slutiil-8"in.block '83', and is. threadedk 'in an end block.- 4l 261 carried by link. 'l 2.'. As. thefscrewf'l .Ul-isi turned,v b1oekf183 moves along slot {'-Iritovary the. eiectivelength of'link 'i2'. Graduations .ILZZmaybe employed, either to indicate the s effective: length; ofi the link or to indicateLtheratin of R ftoiro.

The edle-,et Lof varying :the relative; lengthsv of these llinks isito vary the-ratiomi- Eto 'ru and; the

eiect of varying the lengthoiz 'Siis-:toivaryf ro alone.y Thus, a ratio-:of: tolnmay be: set 'into the instrument, Vsay -R/ruzflll, or zsuchf ratio may bei l'ouilt.` int'otthe'. instrument. Then'. allnthatr--isjyr l necessary.- is to vs'electrtlieiY proper-Value. Vofro (1 ,and that Fig. 7.'.whiie showing adiust'ableglegs and 39- may' Well' be; employed with legs of `fixed length asin Fig. v9 suchi length Ybeingadapted ftb cover aparti'curarv desired range .whichthe.' instru.-

ment may be calledxupom to provide.- Y

It'will be observed that-the DasiccOncept of `my' invention 'residessirr Vmaterializing;two` inter.- cepts upon 'a .straight line-and .inivaryingfgsaid intercepts so thatthe product: thereof remains constant. At the sameftime, one; intercept is varied as a= function'f ofthe Sangle-ofl `rotation.v of said straight. linegin--raceorclancewith the basic equation so that the combined-rotation and-translation oil'a: pointt materializing.,` ai terminus ofzthe other intercept, :traverses the' desired arc;` Nu.- merous alterations, substitutions and modications Within the. aforesaidbasi-c: concept, will be obvious or will: readily'occur:to--thosefskilled in the art. Therefore, I do notzwish.to`-belimited to the precise Idetails ofe construct-ion. showniorthey are illustrativeonly; 'Fo-fthecontrary;k Iiwishto.

reserve all. such .changes,modications, and .subbstitutions of equivalents. Aasiallrwithin *the scope of the subjoinedc1ai-ms. v Y

It will. befunderstoodethat wl-iile-fall5 modicaktionshavebeen shown assgenerating; an arc-in; a plane, the, same principleslmay.- with but. minor changes. be applied (and., such isY .withintthei con-i- 8 templation cai-this application) toidevices generatingfza surface `of asphere. l

As explained in .my aforesaid.v earlier application, whereas aninstrument with scriber-V has been shown: by wayof illustration,v thee invention is not 'limitedthereto, but maybe employed in any task 4Where lan arc is tobe generated and: includes any device, rfor instance carryingY a.' tool such for' instanceE as agrinder, cutter, miller; polisher, acetylene torch, etcor may be employed as a purely-mechanical movement of: a machine part iii-fan 'arcuate lpath.'

Having now fullyjdisclosed the. invention, what I.l claimand -desire. to.' secu-re by Letters Patent is:

:arc'scriber comprisingAV apair of arms pivoted..together` lfor eoplanar,V angular displacementarelativeone to the other,1a. third arm copivoted vwith saidpair-of arms for similar angular displacement, afiirst .link.-universally pivoted to the distal; end of onefwofsaidpairY of arms, scribermeans .one the. other of said pair of arms, anda second link universally pivoted to the distal end of the third arm, said links having` a mutual pivot Y intermediate their universally mounted ends, said 'pair' ofv arms. having substantially equal effective' lengths reckoned .fromA their point of c0- pivoting,the. plane oi said arms beingnormally positionable to include thev -axis lof said `mutual pivoty when said links are aligned.

2; An arc scriber comprisinga 'pair of'. arms pivoted. together `for substantially eoplanar, angular displacement relative .oneto the other, -a third arm co-pi'voted with said' pair ofV arms. for similar .angular displacement, .a .first link universally pivoted to the distal' end'of oneV of" said pair of arms, and a second Vlink universally pivoted' to 'the distal endof the said third arm, said links having a mutual pivotintermediate their universally pivot'ed' ends,A and'said pair of arms. having -substantially equal effectivelengths, reckoned, .respectively, from v their common pivot. axis, to the center of vthe universal. mounting of. one of said pair. of' arms', andtothe'distal end of the other of :"said'pairl 'of arms.'

STAdeviceasdhclaim 2, sai'dli'nks. having zo-planarvv faces on. the side remote from the `co-'pivotedends'Gr.saidarzns, and thec'enter of .turning of saidl armsfin' their'universal mountings coincidingl with'j said c'o-planar faces.

4; A device 'as in claim 2' wherein said third arm comprises means for varying its effective length.

5. In a Adevice as in claimv 2;'means Vfor varying Vthe lengths ofthe links relativeione '.to the other.

WILFRED THIBODEAU;

REFERENCES lCITED-I The ollowingxeerences are .of record in the le. of' this patent;

UNITED STATES PATENTS Number Name Date 759,566' Stout Y May-10, 1904 880;'796- Horrocks r Mar'.` 3 1908 1-,010;612 Garinger 1"-.. Dec'l 5, 1911 FQREIGNL''PATENTS@ Number n CountryA Date 4,155 Great-[Britain Dea 18, 1873 16,698. Great Britain July,20, 1911 540,266' France n-' Apr...14, 1922 

